If `g(x)=1+3x+5x^2+7x^3+...` to `n` terms then find `int_0^1 g(x)dx`.

If f(x) = x+3x^2+5x^4+7x^8+... to n terms then find the value of f'(1) .

Find int_0^1(4x^3+3x^2-2x+1)dx

int(x x^(3)x^(5)x^(7)…" to n terms")dx=

int_(0)^(1)(3x^(2)+5x)dx

If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=

Evaluate int_(0)^(1)(2-3x+x^2)dx

If f(x)=2x^(2)+7x-9 and g(x)=2x+3 , then find the vlaue of g(g(x)) at x=2

Find the sum of the GP : (i) sqrt(7)+sqrt(21)+3sqrt(7)+... to n terms (ii) 1-1/3+1/3^(2)-1/3^(3)+... to n terms (iii) 1-a+a^(2)-a^(3)+... to n terms (a ne 1) (iv) x^(3)+x^(5)+x^(7)+... to terms (v) x(x+y)+x^(2)(x^(2)+y^(2))+x^(3) (x^(3)+y^(3))+... to n terms